The Reds took the lead when Amir-Hossein Feshangi managed to score the opener in thet 41st minute to send cheers to thousands of his team's fans at Tehran's Azadi Stadium on Thursday.
Ali Daie's men doubled their lead in the early minutes of the second half when Mohammad Nouri netted on a header in the 49th minute.
Rah Ahan then pushed forward and narrowed the gap after Rodriguez Lopez scored in the 56th minute.
However, Nouri scored his second goal of the game 14 minutes after his first goal, once again extending their lead to two goals.
Rah Ahan's Hamid Hedayati scored the second goal for his team in 68th minute, keeping hopes alive for his squad's chance to equalize.
Rah Ahan's coach Rasoul Korbekandi was sent off in the last minutes of the game after he protested a referee's judgment.
Persepolis currently stands in the second place with 12 points. Zob Ahan, coached by Mansour Ebrahimzadeh, tops the table with 13 points after five games.
In other matches on the same day, Shahrdari gained a 3-2 victory over Abadan's Sanate Naft.